Curriculum Shule Direct Kenya Secondary School Form 3 Mathematics Kenya

Mathematics Kenya Form 3 Syllabus

  1. Quadratic Expressions and Equations
    1. Quadratic Expressions and Equations
      1. Factorisation of quadratic expressions
      2. Perfect squares
      3. Completion of the square
      4. Solution of quadratic equations by completing the square
      5. Quadratic formula x=(-b±√(b^2-4ac))/2a
      6. Solution of quadratic equations using the formula
      7. Formation of quadratic equations and solving them
      8. Tables of values for a given quadratic relation
      9. Graphs of quadratics equations
      10. Simultaneous equations - one linear and one quadratic
      11. Application to real life situation: Interpret the discriminant i.e. √(b^2-4ac)
  2. Approximations and Errors
    1. Approximations and Errors
      1. Computing using calculators
      2. Estimations and approximations
      3. Significant figures
      4. Absolute, relative, percentage, round-off and truncation errors
      5. Propagation of errors from simple calculations
      6. Maximum and minimum errors
  3. Trigonometry 2
    1. Trigonometry 2
      1. The unit circle
      2. Trigonometric ratios from the unit circle
      3. Trigonometric ratios of angles greater than 360⁰ and negative angles
      4. Use of trigonometric tables
      5. Radian measure
      6. Simple trigonometric graphs
      7. Derivation of sine and cosine rule
      8. Solution of triangles
      9. Application of sine and cosine rule to real situation
      10. Applications: Conversion of radians to degrees
      11. Apply trigonometry to problems involving bearings and angles of elevation and depression
  4. Surds
    1. Surds
      1. Rational and irrational numbers
      2. Rationalisation of denominators
  5. Further Logarithms
    1. Further Logarithms
      1. Logarithmic notation
      2. The laws of logarithms
      3. Simplification of logarithmic expressions
      4. Solution of logarithmic equations
      5. Further computations using logarithmic laws
  6. Commercial Arithmetic (2)
    1. Commercial Arithmetic (2)
      1. Principal rate and time
      2. Simple interest
      3. Compound interest using step by step method
      4. Derivation of compound interest formula
      5. Calculations using the compound interest formula
      6. Appreciation and depreciation
      7. Calculation of appreciation and depreciation using the compound interest formula
      8. Hire purchase
      9. Income tax
      10. Income tax: Compounding done monthly, quarterly, semi quarterly and annually
  7. Circles, Chords and Tangents
    1. Circles, Chords and Tangents
      1. Arcs, chords and tangents
      2. Lengths of tangents and intersecting chords
      3. Properties of chords
      4. Construction of tangents to a circle
      5. Direct and transverse common tangents to two circle
      6. Angles in alternate segment
      7. Circumscribed, inscribed and escribed circles
      8. Centroid and orthocentre
      9. Apply knowledge of tangents and chords to real life situations
  8. Matrices
    1. Matrices
      1. Matrix
      2. Order of a matrix
      3. Square matrix
      4. Compatibility in addition and multiplication of matrices
      5. Multiplication of a matrix by a scalar
      6. Matrix multiplication
      7. Identity matrix
      8. Determinant of a 2 x 2 matrix
      9. Inverse of a 2 x 2 matrix
      10. Singular matrix
      11. Solutions of simultaneous linear equations in two unknowns
  9. Formulae and Variations
    1. Formulae and Variations
      1. Change of the subject
      2. Direct, inverse, partial and joint variations
      3. Constant of proportionality
      4. Graphs of direct and inverse proportion
      5. Formation of equations on variations from real life situations
  10. Sequence and Series
    1. Sequence and Series
      1. Simple number patterns
      2. Sequences
      3. Arithmetic sequences
      4. Geometric sequence
      5. Determining a term in a sequence
      6. Arithmetic progression (A.P)
      7. Geometric progression (G.P)
      8. Sum of an A.P
      9. Sum of a G.P
      10. Application of A.P and G.P to real life situations
  11. Vectors (2)
    1. Vectors (2)
      1. Coordinates in two and three dimensions
      2. Column and position vectors in three dimensions
      3. Column vectors in terms of unit vectors i, j and k
      4. Magnitude of a vector
      5. Parallel vectors
      6. Collinearity
      7. Proportional division of a line
      8. Ratio theorem
      9. Vector methods in geometry
  12. Binomial Expansions
    1. Binomial Expansions
      1. Binomial expansion up to power four
      2. Pascal's triangle
      3. Coefficient of terms in binomial expansion
      4. Computation using binomial expansion
      5. Evaluation of numerical cases using binomial expansion
  13. Probability
    1. Probability
      1. Probability
      2. Experimental probability
      3. Range of probability measure 0≤ P(x) ≤ 1
      4. Probability space
      5. Theoretical probability
      6. Discrete and continuous probability (simple cases only)
      7. Combined events (mutually exclusive and independent events)
      8. Laws of probability
      9. The tree diagrams
  14. Compound Proportions and Rates of Work
    1. Compound Proportions and Rates of Work
      1. Proportional parts
      2. Compound proportions
      3. Ratios and rates of work
      4. Proportions applied to mixtures
  15. Graphical Methods
    1. Graphical Methods
      1. Tables and graphs of given relations
      2. Graphs of cubic equations
      3. Graphical solutions of cubic equations
      4. Average rate of change
      5. Instantaneous rate of change
      6. Empirical data and their graphs
      7. The line of best fit
      8. Equation of a circle
      9. Finding of the equation of a circle: (x2 + y2 = r2, (x-a)2 + (y-b)2 = r2)
      10. Determining of the centre and radius of a circle

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